LMFDB - Embedded newform 756.2.bq.a.25.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(25,756)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 10, 12]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("756.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bq (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.17
Character	$\chi$	$=$	756.25
Dual form			756.2.bq.a.121.17

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.910101 + 1.47367i) q^{3} +(2.21872 + 0.807546i) q^{5} +(2.43789 + 1.02795i) q^{7} +(-1.34343 + 2.68238i) q^{9} +O(q^{10})$	\(q+(0.910101 + 1.47367i) q^{3} +(2.21872 + 0.807546i) q^{5} +(2.43789 + 1.02795i) q^{7} +(-1.34343 + 2.68238i) q^{9} +(1.96880 - 0.716583i) q^{11} +(-0.243183 - 1.37916i) q^{13} +(0.829194 + 4.00461i) q^{15} -1.68840 q^{17} +2.92222 q^{19} +(0.703873 + 4.52820i) q^{21} +(-0.927800 - 5.26182i) q^{23} +(0.440344 + 0.369493i) q^{25} +(-5.17562 + 0.461458i) q^{27} +(-0.0616446 + 0.349604i) q^{29} +(-4.85924 + 4.07739i) q^{31} +(2.84781 + 2.24920i) q^{33} +(4.57888 + 4.24943i) q^{35} +(2.47603 - 4.28862i) q^{37} +(1.81111 - 1.61355i) q^{39} +(-0.314649 - 1.78446i) q^{41} +(-3.77805 - 3.17016i) q^{43} +(-5.14685 + 4.86656i) q^{45} +(-7.37654 - 6.18965i) q^{47} +(4.88666 + 5.01204i) q^{49} +(-1.53662 - 2.48816i) q^{51} +(-5.23915 + 9.07447i) q^{53} +4.94687 q^{55} +(2.65952 + 4.30640i) q^{57} +(-0.0133078 - 0.0754723i) q^{59} +(11.2700 + 9.45663i) q^{61} +(-6.03249 + 5.15840i) q^{63} +(0.574182 - 3.25635i) q^{65} +(6.85380 + 2.49458i) q^{67} +(6.90981 - 6.15606i) q^{69} +(-5.23209 - 9.06224i) q^{71} +(1.60142 + 2.77374i) q^{73} +(-0.143754 + 0.985200i) q^{75} +(5.53633 + 0.276860i) q^{77} +(-12.0873 + 4.39941i) q^{79} +(-5.39038 - 7.20721i) q^{81} +(-0.792643 + 4.49530i) q^{83} +(-3.74609 - 1.36346i) q^{85} +(-0.571305 + 0.227331i) q^{87} -3.52003 q^{89} +(0.824847 - 3.61223i) q^{91} +(-10.4311 - 3.45011i) q^{93} +(6.48358 + 2.35983i) q^{95} +(6.21569 + 5.21558i) q^{97} +(-0.722794 + 6.24375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 6 q^{9}+O(q^{10}) $ 144 * q + 6 * q^9	$ 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) $ 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.910101	+	1.47367i	0.525447	+	0.850826i
$3$	0.910101	+	1.47367i	0.525447	+	0.850826i
$4$		0			0
$5$	2.21872	+	0.807546i	0.992240	+	0.361146i	0.786587	−	0.617479i	$-0.211846\pi$
$5$	2.21872	+	0.807546i	0.992240	+	0.361146i	0.205653	+	0.978625i	$0.434068\pi$
$6$		0			0
$7$	2.43789	+	1.02795i	0.921437	+	0.388527i
$7$	2.43789	+	1.02795i	0.921437	+	0.388527i
$8$		0			0
$9$	−1.34343	+	2.68238i	−0.447811	+	0.894128i
$10$		0			0
$11$	1.96880	−	0.716583i	0.593614	−	0.216058i	−0.0277040	−	0.999616i	$-0.508820\pi$
$11$	1.96880	−	0.716583i	0.593614	−	0.216058i	0.621318	+	0.783558i	$0.286597\pi$
$12$		0			0
$13$	−0.243183	−	1.37916i	−0.0674469	−	0.382511i	−0.999781	−	0.0209132i	$-0.993343\pi$
$13$	−0.243183	−	1.37916i	−0.0674469	−	0.382511i	0.932334	−	0.361597i	$-0.117768\pi$
$14$		0			0
$15$	0.829194	+	4.00461i	0.214097	+	1.03399i
$16$		0			0
$17$	−1.68840			−0.409498			−0.204749	−	0.978815i	$-0.565638\pi$
$17$	−1.68840			−0.409498			−0.204749	+	0.978815i	$0.565638\pi$
$18$		0			0
$19$	2.92222			0.670403			0.335202	−	0.942146i	$-0.391196\pi$
$19$	2.92222			0.670403			0.335202	+	0.942146i	$0.391196\pi$
$20$		0			0
$21$	0.703873	+	4.52820i	0.153598	+	0.988133i
$22$		0			0
$23$	−0.927800	−	5.26182i	−0.193460	−	1.09716i	−0.914595	−	0.404370i	$-0.867491\pi$
$23$	−0.927800	−	5.26182i	−0.193460	−	1.09716i	0.721136	−	0.692794i	$-0.243620\pi$
$24$		0			0
$25$	0.440344	+	0.369493i	0.0880689	+	0.0738986i
$26$		0			0
$27$	−5.17562	+	0.461458i	−0.996049	+	0.0888075i
$28$		0			0
$29$	−0.0616446	+	0.349604i	−0.0114471	+	0.0649198i	−0.989996	−	0.141094i	$-0.954938\pi$
$29$	−0.0616446	+	0.349604i	−0.0114471	+	0.0649198i	0.978549	+	0.206014i	$0.0660492\pi$
$30$		0			0
$31$	−4.85924	+	4.07739i	−0.872745	+	0.732320i	−0.964674	−	0.263445i	$-0.915141\pi$
$31$	−4.85924	+	4.07739i	−0.872745	+	0.732320i	0.0919289	+	0.995766i	$0.470697\pi$
$32$		0			0
$33$	2.84781	+	2.24920i	0.495741	+	0.391536i
$34$		0			0
$35$	4.57888	+	4.24943i	0.773972	+	0.718285i
$36$		0			0
$37$	2.47603	−	4.28862i	0.407057	−	0.705044i	−0.587501	−	0.809223i	$-0.699888\pi$
$37$	2.47603	−	4.28862i	0.407057	−	0.705044i	0.994559	+	0.104179i	$0.0332215\pi$
$38$		0			0
$39$	1.81111	−	1.61355i	0.290010	−	0.258375i
$40$		0			0
$41$	−0.314649	−	1.78446i	−0.0491399	−	0.278686i	0.950330	−	0.311244i	$-0.100746\pi$
$41$	−0.314649	−	1.78446i	−0.0491399	−	0.278686i	−0.999470	+	0.0325579i	$0.989635\pi$
$42$		0			0
$43$	−3.77805	−	3.17016i	−0.576148	−	0.483445i	0.307532	−	0.951538i	$-0.400497\pi$
$43$	−3.77805	−	3.17016i	−0.576148	−	0.483445i	−0.883680	+	0.468092i	$0.844941\pi$
$44$		0			0
$45$	−5.14685	+	4.86656i	−0.767246	+	0.725464i
$46$		0			0
$47$	−7.37654	−	6.18965i	−1.07598	−	0.902853i	−0.0803979	−	0.996763i	$-0.525619\pi$
$47$	−7.37654	−	6.18965i	−1.07598	−	0.902853i	−0.995581	+	0.0939096i	$0.970064\pi$
$48$		0			0
$49$	4.88666	+	5.01204i	0.698094	+	0.716006i
$50$		0			0
$51$	−1.53662	−	2.48816i	−0.215169	−	0.348412i
$52$		0			0
$53$	−5.23915	+	9.07447i	−0.719652	+	1.24647i	0.241485	+	0.970405i	$0.422365\pi$
$53$	−5.23915	+	9.07447i	−0.719652	+	1.24647i	−0.961138	+	0.276070i	$0.910968\pi$
$54$		0			0
$55$	4.94687			0.667036
$56$		0			0
$57$	2.65952	+	4.30640i	0.352261	+	0.570397i
$58$		0			0
$59$	−0.0133078	−	0.0754723i	−0.00173253	−	0.00982565i	0.983929	−	0.178559i	$-0.0571435\pi$
$59$	−0.0133078	−	0.0754723i	−0.00173253	−	0.00982565i	−0.985662	+	0.168733i	$0.946032\pi$
$60$		0			0
$61$	11.2700	+	9.45663i	1.44297	+	1.21080i	0.937514	+	0.347947i	$0.113121\pi$
$61$	11.2700	+	9.45663i	1.44297	+	1.21080i	0.505458	+	0.862851i	$0.331323\pi$
$62$		0			0
$63$	−6.03249	+	5.15840i	−0.760023	+	0.649897i
$64$		0			0
$65$	0.574182	−	3.25635i	0.0712185	−	0.403900i
$66$		0			0
$67$	6.85380	+	2.49458i	0.837325	+	0.304761i	0.724861	−	0.688895i	$-0.241904\pi$
$67$	6.85380	+	2.49458i	0.837325	+	0.304761i	0.112463	+	0.993656i	$0.464126\pi$
$68$		0			0
$69$	6.90981	−	6.15606i	0.831844	−	0.741102i
$70$		0			0
$71$	−5.23209	−	9.06224i	−0.620935	−	1.07549i	−0.989312	−	0.145814i	$-0.953420\pi$
$71$	−5.23209	−	9.06224i	−0.620935	−	1.07549i	0.368377	−	0.929676i	$-0.379913\pi$
$72$		0			0
$73$	1.60142	+	2.77374i	0.187432	+	0.324642i	0.944393	−	0.328818i	$-0.106650\pi$
$73$	1.60142	+	2.77374i	0.187432	+	0.324642i	−0.756961	+	0.653460i	$0.773317\pi$
$74$		0			0
$75$	−0.143754	+	0.985200i	−0.0165993	+	0.113761i
$76$		0			0
$77$	5.53633	+	0.276860i	0.630923	+	0.0315511i
$78$		0			0
$79$	−12.0873	+	4.39941i	−1.35993	+	0.494972i	−0.916031	−	0.401107i	$-0.868626\pi$
$79$	−12.0873	+	4.39941i	−1.35993	+	0.494972i	−0.443894	+	0.896079i	$0.646403\pi$
$80$		0			0
$81$	−5.39038	−	7.20721i	−0.598931	−	0.800801i
$82$		0			0
$83$	−0.792643	+	4.49530i	−0.0870039	+	0.493423i	0.909902	+	0.414823i	$0.136156\pi$
$83$	−0.792643	+	4.49530i	−0.0870039	+	0.493423i	−0.996906	+	0.0786008i	$0.974955\pi$
$84$		0			0
$85$	−3.74609	−	1.36346i	−0.406320	−	0.147888i
$86$		0			0
$87$	−0.571305	+	0.227331i	−0.0612504	+	0.0243724i
$88$		0			0
$89$	−3.52003			−0.373122			−0.186561	−	0.982443i	$-0.559734\pi$
$89$	−3.52003			−0.373122			−0.186561	+	0.982443i	$0.559734\pi$
$90$		0			0
$91$	0.824847	−	3.61223i	0.0864674	−	0.378664i
$92$		0			0
$93$	−10.4311	−	3.45011i	−1.08166	−	0.357759i
$94$		0			0
$95$	6.48358	+	2.35983i	0.665201	+	0.242113i
$96$		0			0
$97$	6.21569	+	5.21558i	0.631108	+	0.529562i	0.901273	−	0.433252i	$-0.142634\pi$
$97$	6.21569	+	5.21558i	0.631108	+	0.529562i	−0.270165	+	0.962814i	$0.587078\pi$
$98$		0			0
$99$	−0.722794	+	6.24375i	−0.0726435	+	0.627521i
$100$		0			0
$101$	−0.0664263	+	0.376722i	−0.00660966	+	0.0374853i	−0.987934	−	0.154874i	$-0.950503\pi$
$101$	−0.0664263	+	0.376722i	−0.00660966	+	0.0374853i	0.981325	+	0.192359i	$0.0616139\pi$
$102$		0			0
$103$	5.84496	+	2.12739i	0.575921	+	0.209618i	0.613526	−	0.789675i	$-0.289751\pi$
$103$	5.84496	+	2.12739i	0.575921	+	0.209618i	−0.0376050	+	0.999293i	$0.511973\pi$
$104$		0			0
$105$	−2.09503	+	10.6152i	−0.204454	+	1.03594i
$106$		0			0
$107$	−7.86467	−	13.6220i	−0.760306	−	1.31689i	−0.942693	−	0.333662i	$-0.891716\pi$
$107$	−7.86467	−	13.6220i	−0.760306	−	1.31689i	0.182387	−	0.983227i	$-0.441618\pi$
$108$		0			0
$109$	2.86702	−	4.96583i	0.274611	−	0.475640i	−0.695426	−	0.718598i	$-0.744784\pi$
$109$	2.86702	−	4.96583i	0.274611	−	0.475640i	0.970037	+	0.242958i	$0.0781176\pi$
$110$		0			0
$111$	8.57347	−	0.254205i	0.813757	−	0.0241281i
$112$		0			0
$113$	1.85167	−	1.55373i	0.174190	−	0.146163i	−0.551524	−	0.834159i	$-0.685954\pi$
$113$	1.85167	−	1.55373i	0.174190	−	0.146163i	0.725715	+	0.687996i	$0.241509\pi$
$114$		0			0
$115$	2.19064	−	12.4237i	0.204278	−	1.15852i
$116$		0			0
$117$	4.02614	+	1.20050i	0.372217	+	0.110986i
$118$		0			0
$119$	−4.11615	−	1.73559i	−0.377327	−	0.159101i
$120$		0			0
$121$	−5.06382	+	4.24905i	−0.460347	+	0.386277i
$122$		0			0
$123$	2.34336	−	2.08773i	0.211293	−	0.188245i
$124$		0			0
$125$	−5.22415	−	9.04850i	−0.467262	−	0.809322i
$126$		0			0
$127$	9.46831	−	16.3996i	0.840177	−	1.45523i	−0.0495683	−	0.998771i	$-0.515785\pi$
$127$	9.46831	−	16.3996i	0.840177	−	1.45523i	0.889745	−	0.456458i	$-0.150882\pi$
$128$		0			0
$129$	1.23338	−	8.45279i	0.108593	−	0.744227i
$130$		0			0
$131$	−2.91160	−	16.5125i	−0.254388	−	1.44271i	−0.797639	−	0.603135i	$-0.793918\pi$
$131$	−2.91160	−	16.5125i	−0.254388	−	1.44271i	0.543251	−	0.839570i	$-0.317193\pi$
$132$		0			0
$133$	7.12407	+	3.00388i	0.617735	+	0.260470i
$134$		0			0
$135$	−11.8559	−	3.15571i	−1.02039	−	0.271600i
$136$		0			0
$137$	8.15433	+	6.84229i	0.696671	+	0.584576i	0.920824	−	0.389977i	$-0.127517\pi$
$137$	8.15433	+	6.84229i	0.696671	+	0.584576i	−0.224153	+	0.974554i	$0.571962\pi$
$138$		0			0
$139$	1.04189	+	0.379216i	0.0883716	+	0.0321646i	0.385828	−	0.922571i	$-0.373916\pi$
$139$	1.04189	+	0.379216i	0.0883716	+	0.0321646i	−0.297456	+	0.954736i	$0.596138\pi$
$140$		0			0
$141$	2.40814	−	16.5038i	0.202802	−	1.38987i
$142$		0			0
$143$	−1.46706	−	2.54103i	−0.122682	−	0.212491i
$144$		0			0
$145$	−0.419093	+	0.725891i	−0.0348038	+	0.0602820i
$146$		0			0
$147$	−2.93877	+	11.7628i	−0.242386	+	0.970180i
$148$		0			0
$149$	−13.5127	+	11.3385i	−1.10700	+	0.928884i	−0.997876	−	0.0651440i	$-0.979249\pi$
$149$	−13.5127	+	11.3385i	−1.10700	+	0.928884i	−0.109125	+	0.994028i	$0.534805\pi$
$150$		0			0
$151$	16.3714	−	5.95868i	1.33228	−	0.484911i	0.424908	−	0.905236i	$-0.360306\pi$
$151$	16.3714	−	5.95868i	1.33228	−	0.484911i	0.907373	+	0.420326i	$0.138084\pi$
$152$		0			0
$153$	2.26826	−	4.52895i	0.183378	−	0.366144i
$154$		0			0
$155$	−14.0740	+	5.12250i	−1.13045	+	0.411449i
$156$		0			0
$157$	−0.536877	−	3.04478i	−0.0428474	−	0.243000i	0.955860	−	0.293821i	$-0.0949271\pi$
$157$	−0.536877	−	3.04478i	−0.0428474	−	0.243000i	−0.998708	+	0.0508216i	$0.983816\pi$
$158$		0			0
$159$	−18.1410	+	0.537884i	−1.43867	+	0.0426570i
$160$		0			0
$161$	3.14698	−	13.7815i	0.248017	−	1.08613i
$162$		0			0
$163$	3.38809	+	5.86835i	0.265376	+	0.459645i	0.967662	−	0.252250i	$-0.0811706\pi$
$163$	3.38809	+	5.86835i	0.265376	+	0.459645i	−0.702286	+	0.711895i	$0.747837\pi$
$164$		0			0
$165$	4.50215	+	7.29008i	0.350492	+	0.567532i
$166$		0			0
$167$	15.0245	−	12.6071i	1.16263	−	0.975564i	0.162694	−	0.986677i	$-0.447982\pi$
$167$	15.0245	−	12.6071i	1.16263	−	0.975564i	0.999938	+	0.0111125i	$0.00353730\pi$
$168$		0			0
$169$	10.3731	−	3.77548i	0.797927	−	0.290422i
$170$		0			0
$171$	−3.92581	+	7.83852i	−0.300214	+	0.599427i
$172$		0			0
$173$	1.53958	−	8.73141i	0.117052	−	0.663837i	−0.868661	−	0.495407i	$-0.835019\pi$
$173$	1.53958	−	8.73141i	0.117052	−	0.663837i	0.985714	−	0.168430i	$-0.0538698\pi$
$174$		0			0
$175$	0.693695	+	1.35343i	0.0524384	+	0.102310i
$176$		0			0
$177$	0.0991101	−	0.0882987i	0.00744957	−	0.00663694i
$178$		0			0
$179$	−21.9667			−1.64187			−0.820933	−	0.571024i	$-0.806546\pi$
$179$	−21.9667			−1.64187			−0.820933	+	0.571024i	$0.806546\pi$
$180$		0			0
$181$	6.79478	−	11.7689i	0.505052	−	0.874776i	−0.494931	−	0.868932i	$-0.664807\pi$
$181$	6.79478	−	11.7689i	0.505052	−	0.874776i	0.999983	−	0.00584345i	$-0.00186004\pi$
$182$		0			0
$183$	−3.67918	+	25.2148i	−0.271973	+	1.86393i
$184$		0			0
$185$	8.95687	−	7.51571i	0.658522	−	0.552566i
$186$		0			0
$187$	−3.32412	+	1.20988i	−0.243084	+	0.0884753i
$188$		0			0
$189$	−13.0920	−	4.19527i	−0.952301	−	0.305161i
$190$		0			0
$191$	−9.04836	+	3.29333i	−0.654716	+	0.238297i	−0.647953	−	0.761680i	$-0.724375\pi$
$191$	−9.04836	+	3.29333i	−0.654716	+	0.238297i	−0.00676273	+	0.999977i	$0.502153\pi$
$192$		0			0
$193$	−9.90538	+	8.31160i	−0.713005	+	0.598282i	−0.925441	−	0.378893i	$-0.876305\pi$
$193$	−9.90538	+	8.31160i	−0.713005	+	0.598282i	0.212436	+	0.977175i	$0.431860\pi$
$194$		0			0
$195$	5.32136	−	2.11745i	0.381071	−	0.151634i
$196$		0			0
$197$	6.07914	−	10.5294i	0.433121	−	0.750187i	−0.564019	−	0.825762i	$-0.690746\pi$
$197$	6.07914	−	10.5294i	0.433121	−	0.750187i	0.997140	+	0.0755742i	$0.0240790\pi$
$198$		0			0
$199$	−24.2174			−1.71673			−0.858363	−	0.513043i	$-0.828518\pi$
$199$	−24.2174			−1.71673			−0.858363	+	0.513043i	$0.828518\pi$
$200$		0			0
$201$	2.56145	+	12.3706i	0.180671	+	0.872554i
$202$		0			0
$203$	−0.509657	+	0.788930i	−0.0357709	+	0.0553721i
$204$		0			0
$205$	0.742921	−	4.21331i	0.0518878	−	0.294270i
$206$		0			0
$207$	15.3607	+	4.58018i	1.06764	+	0.318345i
$208$		0			0
$209$	5.75326	−	2.09401i	0.397961	−	0.144846i
$210$		0			0
$211$	−11.8517	+	9.94474i	−0.815903	+	0.684624i	−0.952009	−	0.306070i	$-0.900986\pi$
$211$	−11.8517	+	9.94474i	−0.815903	+	0.684624i	0.136106	+	0.990694i	$0.456541\pi$
$212$		0			0
$213$	8.59307	−	15.9579i	0.588787	−	1.09342i
$214$		0			0
$215$	−5.82237	−	10.0846i	−0.397082	−	0.687767i
$216$		0			0
$217$	−16.0376	+	4.94521i	−1.08871	+	0.335703i
$218$		0			0
$219$	−2.63014	+	4.88435i	−0.177728	+	0.330054i
$220$		0			0
$221$	0.410592	+	2.32858i	0.0276194	+	0.156637i
$222$		0			0
$223$	9.20294	−	3.34960i	0.616274	−	0.224306i	−0.0149719	−	0.999888i	$-0.504766\pi$
$223$	9.20294	−	3.34960i	0.616274	−	0.224306i	0.631246	+	0.775582i	$0.282544\pi$
$224$		0			0
$225$	−1.58270	+	0.684784i	−0.105513	+	0.0456523i
$226$		0			0
$227$	−12.9579	+	4.71630i	−0.860047	+	0.313032i	−0.734130	−	0.679009i	$-0.762410\pi$
$227$	−12.9579	+	4.71630i	−0.860047	+	0.313032i	−0.125918	+	0.992041i	$0.540187\pi$
$228$		0			0
$229$	10.4953	−	8.80659i	0.693548	−	0.581956i	−0.226382	−	0.974039i	$-0.572690\pi$
$229$	10.4953	−	8.80659i	0.693548	−	0.581956i	0.919930	+	0.392083i	$0.128245\pi$
$230$		0			0
$231$	4.63061	+	8.41071i	0.304672	+	0.553384i
$232$		0			0
$233$	−3.66435	+	6.34685i	−0.240060	+	0.415796i	−0.960731	−	0.277481i	$-0.910500\pi$
$233$	−3.66435	+	6.34685i	−0.240060	+	0.415796i	0.720671	+	0.693277i	$0.243834\pi$
$234$		0			0
$235$	−11.3680	−	19.6900i	−0.741567	−	1.28443i
$236$		0			0
$237$	−17.4839	−	13.8088i	−1.13570	−	0.896978i
$238$		0			0
$239$	10.8308	+	3.94209i	0.700586	+	0.254992i	0.667661	−	0.744465i	$-0.267296\pi$
$239$	10.8308	+	3.94209i	0.700586	+	0.254992i	0.0329248	+	0.999458i	$0.489518\pi$
$240$		0			0
$241$	5.83320	+	4.89463i	0.375749	+	0.315291i	0.811031	−	0.585003i	$-0.198907\pi$
$241$	5.83320	+	4.89463i	0.375749	+	0.315291i	−0.435282	+	0.900294i	$0.643351\pi$
$242$		0			0
$243$	5.71529	−	14.5029i	0.366636	−	0.930364i
$244$		0			0
$245$	6.79465	+	15.0665i	0.434094	+	0.962563i
$246$		0			0
$247$	−0.710635	−	4.03021i	−0.0452167	−	0.256436i
$248$		0			0
$249$	−7.34600	+	2.92308i	−0.465534	+	0.185243i
$250$		0			0
$251$	7.49729	−	12.9857i	0.473225	−	0.819649i	−0.526306	−	0.850296i	$-0.676423\pi$
$251$	7.49729	−	12.9857i	0.473225	−	0.819649i	0.999530	+	0.0306462i	$0.00975651\pi$
$252$		0			0
$253$	−5.59718	−	9.69460i	−0.351892	−	0.609494i
$254$		0			0
$255$	−1.40001	−	6.76140i	−0.0876723	−	0.423415i
$256$		0			0
$257$	7.74919	−	6.50234i	0.483381	−	0.405605i	−0.368266	−	0.929720i	$-0.620048\pi$
$257$	7.74919	−	6.50234i	0.483381	−	0.405605i	0.851647	+	0.524116i	$0.175604\pi$
$258$		0			0
$259$	10.4448	−	7.90997i	0.649007	−	0.491502i
$260$		0			0
$261$	−0.854957	−	0.635024i	−0.0529205	−	0.0393070i
$262$		0			0
$263$	−4.30518	+	24.4159i	−0.265469	+	1.50555i	0.502229	+	0.864735i	$0.332513\pi$
$263$	−4.30518	+	24.4159i	−0.265469	+	1.50555i	−0.767698	+	0.640812i	$0.778598\pi$
$264$		0			0
$265$	−18.9522	+	15.9028i	−1.16423	+	0.976902i
$266$		0			0
$267$	−3.20358	−	5.18738i	−0.196056	−	0.317462i
$268$		0			0
$269$	8.43234	−	14.6052i	0.514129	−	0.890497i	−0.485737	−	0.874105i	$-0.661449\pi$
$269$	8.43234	−	14.6052i	0.514129	−	0.890497i	0.999866	−	0.0163922i	$-0.00521804\pi$
$270$		0			0
$271$	4.08881	+	7.08203i	0.248378	+	0.430203i	0.963076	−	0.269230i	$-0.0867693\pi$
$271$	4.08881	+	7.08203i	0.248378	+	0.430203i	−0.714698	+	0.699433i	$0.753436\pi$
$272$		0			0
$273$	6.07394	−	2.07194i	0.367612	−	0.125399i
$274$		0			0
$275$	1.13172	+	0.411913i	0.0682453	+	0.0248393i
$276$		0			0
$277$	−1.42784	+	8.09766i	−0.0857903	+	0.486541i	0.911393	+	0.411537i	$0.135008\pi$
$277$	−1.42784	+	8.09766i	−0.0857903	+	0.486541i	−0.997183	+	0.0750038i	$0.976103\pi$
$278$		0			0
$279$	−4.40906	−	18.5121i	−0.263963	−	1.10829i
$280$		0			0
$281$	11.4344	+	9.59463i	0.682121	+	0.572368i	0.916625	−	0.399748i	$-0.130902\pi$
$281$	11.4344	+	9.59463i	0.682121	+	0.572368i	−0.234504	+	0.972115i	$0.575347\pi$
$282$		0			0
$283$	−5.94730	−	2.16464i	−0.353530	−	0.128674i	0.159149	−	0.987255i	$-0.449125\pi$
$283$	−5.94730	−	2.16464i	−0.353530	−	0.128674i	−0.512679	+	0.858580i	$0.671347\pi$
$284$		0			0
$285$	2.42309	+	11.7024i	0.143531	+	0.693188i
$286$		0			0
$287$	1.06725	−	4.67378i	0.0629978	−	0.275884i
$288$		0			0
$289$	−14.1493			−0.832311
$290$		0			0
$291$	−2.02917	+	13.9066i	−0.118952	+	0.815220i
$292$		0			0
$293$	24.8227	+	9.03471i	1.45016	+	0.527813i	0.942635	−	0.333826i	$-0.108340\pi$
$293$	24.8227	+	9.03471i	1.45016	+	0.527813i	0.507521	+	0.861639i	$0.330562\pi$
$294$		0			0
$295$	0.0314211	−	0.178198i	0.00182941	−	0.0103751i
$296$		0			0
$297$	−9.85907	+	4.61728i	−0.572081	+	0.267922i
$298$		0			0
$299$	−7.03127	+	2.55917i	−0.406629	+	0.148001i
$300$		0			0
$301$	−5.95174	−	11.6122i	−0.343053	−	0.669314i
$302$		0			0
$303$	−0.615621	+	0.244964i	−0.0353665	+	0.0140728i
$304$		0			0
$305$	17.3682	+	30.0826i	0.994500	+	1.72252i
$306$		0			0
$307$	−5.16045	−	8.93817i	−0.294523	−	0.510128i	0.680351	−	0.732886i	$-0.261827\pi$
$307$	−5.16045	−	8.93817i	−0.294523	−	0.510128i	−0.974874	+	0.222758i	$0.928494\pi$
$308$		0			0
$309$	2.18442	+	10.5497i	0.124267	+	0.600152i
$310$		0			0
$311$	−10.6993	−	3.89422i	−0.606701	−	0.220821i	0.0203580	−	0.999793i	$-0.493519\pi$
$311$	−10.6993	−	3.89422i	−0.606701	−	0.220821i	−0.627059	+	0.778972i	$0.715742\pi$
$312$		0			0
$313$	−3.91470	+	22.2014i	−0.221272	+	1.25490i	0.648412	+	0.761289i	$0.275433\pi$
$313$	−3.91470	+	22.2014i	−0.221272	+	1.25490i	−0.869685	+	0.493608i	$0.835678\pi$
$314$		0			0
$315$	−17.5500	+	6.57349i	−0.988832	+	0.370374i
$316$		0			0
$317$	8.27537	+	6.94386i	0.464791	+	0.390006i	0.844890	−	0.534940i	$-0.179666\pi$
$317$	8.27537	+	6.94386i	0.464791	+	0.390006i	−0.380099	+	0.924946i	$0.624110\pi$
$318$		0			0
$319$	0.129155	+	0.732473i	0.00723127	+	0.0410106i
$320$		0			0
$321$	12.9168	−	23.9873i	0.720943	−	1.33884i
$322$		0			0
$323$	−4.93389			−0.274529
$324$		0			0
$325$	0.402506	−	0.697161i	0.0223270	−	0.0386715i
$326$		0			0
$327$	9.92730	−	0.294347i	0.548981	−	0.0162774i
$328$		0			0
$329$	−11.6206	−	22.6724i	−0.640664	−	1.24997i
$330$		0			0
$331$	−0.414174	−	0.347533i	−0.0227650	−	0.0191021i	0.631334	−	0.775511i	$-0.282508\pi$
$331$	−0.414174	−	0.347533i	−0.0227650	−	0.0191021i	−0.654099	+	0.756409i	$0.726952\pi$
$332$		0			0
$333$	8.17733	+	12.4031i	0.448115	+	0.679688i
$334$		0			0
$335$	13.1921	+	11.0695i	0.720763	+	0.604792i
$336$		0			0
$337$	1.13311	+	6.42618i	0.0617244	+	0.350057i	0.999991	+	0.00414467i	$0.00131929\pi$
$337$	1.13311	+	6.42618i	0.0617244	+	0.350057i	−0.938267	+	0.345912i	$0.887570\pi$
$338$		0			0
$339$	3.97490	+	1.31470i	0.215887	+	0.0714048i
$340$		0			0
$341$	−6.64507	+	11.5096i	−0.359851	+	0.623280i
$342$		0			0
$343$	6.76105	+	17.2420i	0.365062	+	0.930983i
$344$		0			0
$345$	20.3022	−	8.07855i	1.09303	−	0.434934i
$346$		0			0
$347$	−17.6543	+	14.8137i	−0.947732	+	0.795241i	−0.978914	−	0.204272i	$-0.934517\pi$
$347$	−17.6543	+	14.8137i	−0.947732	+	0.795241i	0.0311824	+	0.999514i	$0.490073\pi$
$348$		0			0
$349$	−5.42541	+	30.7690i	−0.290416	+	1.64703i	0.394857	+	0.918743i	$0.370794\pi$
$349$	−5.42541	+	30.7690i	−0.290416	+	1.64703i	−0.685273	+	0.728287i	$0.740317\pi$
$350$		0			0
$351$	1.89505	+	7.02580i	0.101150	+	0.375009i
$352$		0			0
$353$	12.7360	+	10.6868i	0.677870	+	0.568800i	0.915383	−	0.402584i	$-0.131888\pi$
$353$	12.7360	+	10.6868i	0.677870	+	0.568800i	−0.237513	+	0.971384i	$0.576332\pi$
$354$		0			0
$355$	−4.29033	−	24.3317i	−0.227707	−	1.29139i
$356$		0			0
$357$	−1.18842	−	7.64542i	−0.0628980	−	0.404639i
$358$		0			0
$359$	15.6681			0.826931			0.413465	−	0.910520i	$-0.364318\pi$
$359$	15.6681			0.826931			0.413465	+	0.910520i	$0.364318\pi$
$360$		0			0
$361$	−10.4606			−0.550559
$362$		0			0
$363$	−10.8703	−	3.59536i	−0.570543	−	0.188707i
$364$		0			0
$365$	1.31317	+	7.44736i	0.0687345	+	0.389812i
$366$		0			0
$367$	31.6938	−	11.5356i	1.65440	−	0.602154i	0.664935	−	0.746901i	$-0.268459\pi$
$367$	31.6938	−	11.5356i	1.65440	−	0.602154i	0.989469	+	0.144748i	$0.0462371\pi$
$368$		0			0
$369$	5.20933	+	1.55330i	0.271187	+	0.0808615i
$370$		0			0
$371$	−22.1005	+	16.7370i	−1.14740	+	0.868944i
$372$		0			0
$373$	−25.4054	−	9.24679i	−1.31544	−	0.478781i	−0.413445	−	0.910529i	$-0.635675\pi$
$373$	−25.4054	−	9.24679i	−1.31544	−	0.478781i	−0.901994	+	0.431748i	$0.857897\pi$
$374$		0			0
$375$	8.58003	−	15.9337i	0.443071	−	0.822815i
$376$		0			0
$377$	0.497151			0.0256046
$378$		0			0
$379$	18.0692			0.928151			0.464075	−	0.885796i	$-0.346387\pi$
$379$	18.0692			0.928151			0.464075	+	0.885796i	$0.346387\pi$
$380$		0			0
$381$	32.7848	−	0.972077i	1.67962	−	0.0498010i
$382$		0			0
$383$	29.9218	+	10.8907i	1.52893	+	0.556486i	0.963360	−	0.268212i	$-0.0864326\pi$
$383$	29.9218	+	10.8907i	1.52893	+	0.556486i	0.565573	+	0.824698i	$0.308655\pi$
$384$		0			0
$385$	12.0600	+	5.08511i	0.614632	+	0.259161i
$386$		0			0
$387$	13.5792	−	5.87529i	0.690268	−	0.298658i
$388$		0			0
$389$	15.9687	−	5.81212i	0.809643	−	0.294686i	0.0961669	−	0.995365i	$-0.469342\pi$
$389$	15.9687	−	5.81212i	0.809643	−	0.294686i	0.713477	+	0.700679i	$0.247120\pi$
$390$		0			0
$391$	1.56650	+	8.88407i	0.0792214	+	0.449287i
$392$		0			0
$393$	21.6842	−	19.3188i	1.09382	−	0.974505i
$394$		0			0
$395$	−30.3710			−1.52813
$396$		0			0
$397$	9.13726			0.458586			0.229293	−	0.973357i	$-0.426359\pi$
$397$	9.13726			0.458586			0.229293	+	0.973357i	$0.426359\pi$
$398$		0			0
$399$	2.05687	+	13.2324i	0.102972	+	0.662448i
$400$		0			0
$401$	3.16249	+	17.9354i	0.157927	+	0.895650i	0.956061	+	0.293169i	$0.0947099\pi$
$401$	3.16249	+	17.9354i	0.157927	+	0.895650i	−0.798133	+	0.602481i	$0.794179\pi$
$402$		0			0
$403$	6.80506	+	5.71012i	0.338984	+	0.284442i
$404$		0			0
$405$	−6.13955	−	20.3437i	−0.305077	−	1.01089i
$406$		0			0
$407$	1.80166	−	10.2177i	0.0893048	−	0.506472i
$408$		0			0
$409$	−10.0599	+	8.44129i	−0.497432	+	0.417395i	−0.856681	−	0.515847i	$-0.827477\pi$
$409$	−10.0599	+	8.44129i	−0.497432	+	0.417395i	0.359249	+	0.933242i	$0.383033\pi$
$410$		0			0
$411$	−2.66205	+	18.2440i	−0.131309	+	0.899910i
$412$		0			0
$413$	0.0451383	−	0.197673i	0.00222111	−	0.00972686i
$414$		0			0
$415$	−5.38881	+	9.33370i	−0.264526	+	0.458173i
$416$		0			0
$417$	0.389381	+	1.88053i	0.0190681	+	0.0920897i
$418$		0			0
$419$	1.08860	+	6.17376i	0.0531816	+	0.301608i	0.999784	−	0.0207963i	$-0.00662015\pi$
$419$	1.08860	+	6.17376i	0.0531816	+	0.301608i	−0.946602	+	0.322404i	$0.895509\pi$
$420$		0			0
$421$	−10.8242	−	9.08261i	−0.527541	−	0.442659i	0.339710	−	0.940530i	$-0.389671\pi$
$421$	−10.8242	−	9.08261i	−0.527541	−	0.442659i	−0.867251	+	0.497871i	$0.834115\pi$
$422$		0			0
$423$	26.5129	−	11.4713i	1.28910	−	0.557755i
$424$		0			0
$425$	−0.743479	−	0.623853i	−0.0360640	−	0.0302613i
$426$		0			0
$427$	17.7541	+	34.6392i	0.859182	+	1.67631i
$428$		0			0
$429$	2.40947	−	4.47456i	0.116330	−	0.216034i
$430$		0			0
$431$	−0.413066	+	0.715451i	−0.0198967	+	0.0344621i	−0.875802	−	0.482670i	$-0.839667\pi$
$431$	−0.413066	+	0.715451i	−0.0198967	+	0.0344621i	0.855906	+	0.517132i	$0.173000\pi$
$432$		0			0
$433$	−23.5919			−1.13376			−0.566878	−	0.823802i	$-0.691849\pi$
$433$	−23.5919			−1.13376			−0.566878	+	0.823802i	$0.691849\pi$
$434$		0			0
$435$	−1.45114	+	0.0430268i	−0.0695770	+	0.00206298i
$436$		0			0
$437$	−2.71124	−	15.3762i	−0.129696	−	0.735543i
$438$		0			0
$439$	−1.85120	−	1.55334i	−0.0883528	−	0.0741368i	0.597541	−	0.801838i	$-0.296144\pi$
$439$	−1.85120	−	1.55334i	−0.0883528	−	0.0741368i	−0.685894	+	0.727701i	$0.740589\pi$
$440$		0			0
$441$	−20.0091	+	6.37455i	−0.952815	+	0.303550i
$442$		0			0
$443$	−5.26617	+	29.8659i	−0.250203	+	1.41897i	0.557889	+	0.829916i	$0.311612\pi$
$443$	−5.26617	+	29.8659i	−0.250203	+	1.41897i	−0.808092	+	0.589056i	$0.799500\pi$
$444$		0			0
$445$	−7.80994	−	2.84259i	−0.370227	−	0.134752i
$446$		0			0
$447$	−29.0071	−	9.59412i	−1.37199	−	0.453786i
$448$		0			0
$449$	−6.74806	−	11.6880i	−0.318461	−	0.551590i	0.661706	−	0.749763i	$-0.269833\pi$
$449$	−6.74806	−	11.6880i	−0.318461	−	0.551590i	−0.980167	+	0.198173i	$0.936499\pi$
$450$		0			0
$451$	−1.89820	−	3.28777i	−0.0893826	−	0.154815i
$452$		0			0
$453$	23.6807	+	18.7030i	1.11262	+	0.878745i
$454$		0			0
$455$	4.74714	−	7.34841i	0.222549	−	0.344499i
$456$		0			0
$457$	−13.1475	+	4.78531i	−0.615015	+	0.223847i	−0.630696	−	0.776030i	$-0.717231\pi$
$457$	−13.1475	+	4.78531i	−0.615015	+	0.223847i	0.0156809	+	0.999877i	$0.495008\pi$
$458$		0			0
$459$	8.73854	−	0.779127i	0.407880	−	0.0363665i
$460$		0			0
$461$	−2.35238	+	13.3410i	−0.109561	+	0.621354i	0.879738	+	0.475458i	$0.157718\pi$
$461$	−2.35238	+	13.3410i	−0.109561	+	0.621354i	−0.989300	+	0.145896i	$0.953394\pi$
$462$		0			0
$463$	36.0211	+	13.1106i	1.67404	+	0.609302i	0.992475	−	0.122451i	$-0.0390754\pi$
$463$	36.0211	+	13.1106i	1.67404	+	0.609302i	0.681570	+	0.731753i	$0.261298\pi$
$464$		0			0
$465$	−20.3576	−	16.0784i	−0.944062	−	0.745619i
$466$		0			0
$467$	−2.31882			−0.107302			−0.0536511	−	0.998560i	$-0.517086\pi$
$467$	−2.31882			−0.107302			−0.0536511	+	0.998560i	$0.517086\pi$
$468$		0			0
$469$	14.1445	+	13.1268i	0.653134	+	0.606141i
$470$		0			0
$471$	3.99840	−	3.56224i	0.184237	−	0.164139i
$472$		0			0
$473$	−9.70990	−	3.53412i	−0.446462	−	0.162499i
$474$		0			0
$475$	1.28678	+	1.07974i	0.0590417	+	0.0495419i
$476$		0			0
$477$	−17.3028	−	26.2444i	−0.792240	−	1.20165i
$478$		0			0
$479$	−1.88929	+	10.7147i	−0.0863237	+	0.489566i	0.910739	+	0.412981i	$0.135513\pi$
$479$	−1.88929	+	10.7147i	−0.0863237	+	0.489566i	−0.997063	+	0.0765844i	$0.975599\pi$
$480$		0			0
$481$	−6.51682	−	2.37193i	−0.297142	−	0.108151i
$482$		0			0
$483$	23.1735	−	7.90491i	1.05443	−	0.359686i
$484$		0			0
$485$	9.57902	+	16.5914i	0.434961	+	0.753374i
$486$		0			0
$487$	8.67338	−	15.0227i	0.393028	−	0.680745i	−0.599819	−	0.800136i	$-0.704761\pi$
$487$	8.67338	−	15.0227i	0.393028	−	0.680745i	0.992847	+	0.119391i	$0.0380941\pi$
$488$		0			0
$489$	−5.56453	+	10.3337i	−0.251637	+	0.467308i
$490$		0			0
$491$	−21.1809	+	17.7729i	−0.955882	+	0.802080i	−0.980278	−	0.197622i	$-0.936678\pi$
$491$	−21.1809	+	17.7729i	−0.955882	+	0.802080i	0.0243964	+	0.999702i	$0.492234\pi$
$492$		0			0
$493$	0.104081	−	0.590273i	0.00468757	−	0.0265845i
$494$		0			0
$495$	−6.64579	+	13.2694i	−0.298706	+	0.596416i
$496$		0			0
$497$	−3.43979	−	27.4711i	−0.154296	−	1.23225i
$498$		0			0
$499$	−15.4968	+	13.0034i	−0.693733	+	0.582111i	−0.919983	−	0.391958i	$-0.871798\pi$
$499$	−15.4968	+	13.0034i	−0.693733	+	0.582111i	0.226250	+	0.974069i	$0.427353\pi$
$500$		0			0
$501$	32.2525	+	10.6675i	1.44094	+	0.476591i
$502$		0			0
$503$	−5.72001	−	9.90735i	−0.255043	−	0.441747i	0.709864	−	0.704338i	$-0.248756\pi$
$503$	−5.72001	−	9.90735i	−0.255043	−	0.441747i	−0.964907	+	0.262591i	$0.915423\pi$
$504$		0			0
$505$	−0.451602	+	0.782197i	−0.0200960	+	0.0348073i
$506$		0			0
$507$	15.0044	+	11.8504i	0.666367	+	0.526296i
$508$		0			0
$509$	6.37655	+	36.1632i	0.282636	+	1.60291i	0.713611	+	0.700542i	$0.247058\pi$
$509$	6.37655	+	36.1632i	0.282636	+	1.60291i	−0.430975	+	0.902364i	$0.641830\pi$
$510$		0			0
$511$	1.05284	+	8.40825i	0.0465749	+	0.371959i
$512$		0			0
$513$	−15.1243	+	1.34848i	−0.667755	+	0.0595369i
$514$		0			0
$515$	11.2503	+	9.44015i	0.495749	+	0.415983i
$516$		0			0
$517$	−18.9583	−	6.90026i	−0.833785	−	0.303473i
$518$		0			0
$519$	14.2684	−	5.67762i	0.626315	−	0.249220i
$520$		0			0
$521$	19.9750	+	34.5977i	0.875119	+	1.51575i	0.856636	+	0.515922i	$0.172551\pi$
$521$	19.9750	+	34.5977i	0.875119	+	1.51575i	0.0184838	+	0.999829i	$0.494116\pi$
$522$		0			0
$523$	10.0938	−	17.4830i	0.441371	−	0.764478i	−0.556420	−	0.830901i	$-0.687825\pi$
$523$	10.0938	−	17.4830i	0.441371	−	0.764478i	0.997792	+	0.0664234i	$0.0211588\pi$
$524$		0			0
$525$	−1.36319	+	2.25404i	−0.0594945	+	0.0983745i
$526$		0			0
$527$	8.20436	−	6.88428i	0.357388	−	0.299884i
$528$		0			0
$529$	−5.21296	+	1.89736i	−0.226650	+	0.0824940i
$530$		0			0
$531$	0.220324	+	0.0656953i	0.00956124	+	0.00285093i
$532$		0			0
$533$	−2.38455	+	0.867904i	−0.103286	+	0.0375931i
$534$		0			0
$535$	−6.44906	−	36.5744i	−0.278817	−	1.58125i
$536$		0			0
$537$	−19.9919	−	32.3717i	−0.862714	−	1.39694i
$538$		0			0
$539$	13.2124	+	6.36599i	0.569098	+	0.274203i
$540$		0			0
$541$	−8.11680	−	14.0587i	−0.348969	−	0.604431i	0.637098	−	0.770783i	$-0.280135\pi$
$541$	−8.11680	−	14.0587i	−0.348969	−	0.604431i	−0.986067	+	0.166351i	$0.946801\pi$
$542$		0			0
$543$	23.5275	−	0.697595i	1.00966	−	0.0299367i
$544$		0			0
$545$	10.3712	−	8.70251i	0.444255	−	0.372775i
$546$		0			0
$547$	−8.69805	+	3.16583i	−0.371902	+	0.135361i	−0.521208	−	0.853430i	$-0.674518\pi$
$547$	−8.69805	+	3.16583i	−0.371902	+	0.135361i	0.149306	+	0.988791i	$0.452296\pi$
$548$		0			0
$549$	−40.5068	+	17.5261i	−1.72879	+	0.747994i
$550$		0			0
$551$	−0.180139	+	1.02162i	−0.00767419	+	0.0435225i
$552$		0			0
$553$	−33.9899	−	1.69976i	−1.44540	−	0.0722812i
$554$		0			0
$555$	19.2274	+	6.35946i	0.816156	+	0.269944i
$556$		0			0
$557$	−44.5513			−1.88770			−0.943850	−	0.330374i	$-0.892825\pi$
$557$	−44.5513			−1.88770			−0.943850	+	0.330374i	$0.892825\pi$
$558$		0			0
$559$	−3.45341	+	5.98148i	−0.146064	+	0.252990i
$560$		0			0
$561$	−4.80826	−	3.79756i	−0.203005	−	0.160333i
$562$		0			0
$563$	7.16562	−	6.01267i	0.301995	−	0.253404i	−0.479179	−	0.877717i	$-0.659066\pi$
$563$	7.16562	−	6.01267i	0.301995	−	0.253404i	0.781174	+	0.624313i	$0.214621\pi$
$564$		0			0
$565$	5.36304	−	1.95199i	0.225625	−	0.0821206i
$566$		0			0
$567$	−5.73255	−	23.1114i	−0.240745	−	0.970589i
$568$		0			0
$569$	−5.96140	+	2.16977i	−0.249915	+	0.0909616i	−0.463940	−	0.885867i	$-0.653565\pi$
$569$	−5.96140	+	2.16977i	−0.249915	+	0.0909616i	0.214025	+	0.976828i	$0.431343\pi$
$570$		0			0
$571$	−24.8254	+	20.8310i	−1.03891	+	0.871749i	−0.991884	−	0.127144i	$-0.959419\pi$
$571$	−24.8254	+	20.8310i	−1.03891	+	0.871749i	−0.0470262	+	0.998894i	$0.514974\pi$
$572$		0			0
$573$	−13.0882	−	10.3371i	−0.546768	−	0.431837i
$574$		0			0
$575$	1.53565	−	2.65983i	0.0640411	−	0.110922i
$576$		0			0
$577$	28.1252			1.17087			0.585434	−	0.810720i	$-0.300924\pi$
$577$	28.1252			1.17087			0.585434	+	0.810720i	$0.300924\pi$
$578$		0			0
$579$	−21.2635	−	7.03291i	−0.883680	−	0.292278i
$580$		0			0
$581$	−6.55330	+	10.1443i	−0.271877	+	0.420855i
$582$		0			0
$583$	−3.81220	+	21.6201i	−0.157885	+	0.895412i
$584$		0			0
$585$	7.96340	+	5.91486i	0.329246	+	0.244549i
$586$		0			0
$587$	39.6831	−	14.4435i	1.63790	−	0.596146i	0.651227	−	0.758883i	$-0.274254\pi$
$587$	39.6831	−	14.4435i	1.63790	−	0.596146i	0.986669	+	0.162737i	$0.0520322\pi$
$588$		0			0
$589$	−14.1998	+	11.9150i	−0.585092	+	0.490950i
$590$		0			0
$591$	21.0495	−	0.624123i	0.865861	−	0.0256730i
$592$		0			0
$593$	−17.2108	−	29.8099i	−0.706762	−	1.22415i	−0.966052	−	0.258348i	$-0.916822\pi$
$593$	−17.2108	−	29.8099i	−0.706762	−	1.22415i	0.259290	−	0.965800i	$-0.416512\pi$
$594$		0			0
$595$	−7.73100	−	7.17475i	−0.316940	−	0.294136i
$596$		0			0
$597$	−22.0403	−	35.6886i	−0.902049	−	1.46064i
$598$		0			0
$599$	−4.64928	−	26.3674i	−0.189965	−	1.07734i	−0.919409	−	0.393303i	$-0.871332\pi$
$599$	−4.64928	−	26.3674i	−0.189965	−	1.07734i	0.729444	−	0.684040i	$-0.239779\pi$
$600$		0			0
$601$	−41.7395	+	15.1920i	−1.70259	+	0.619693i	−0.996116	−	0.0880453i	$-0.971938\pi$
$601$	−41.7395	+	15.1920i	−1.70259	+	0.619693i	−0.706475	+	0.707738i	$0.749716\pi$
$602$		0			0
$603$	−15.8990	+	15.0332i	−0.647459	+	0.612200i
$604$		0			0
$605$	−14.6665	+	5.33816i	−0.596277	+	0.217027i
$606$		0			0
$607$	31.7320	−	26.6263i	1.28796	−	1.08073i	0.295866	−	0.955229i	$-0.404392\pi$
$607$	31.7320	−	26.6263i	1.28796	−	1.08073i	0.992094	−	0.125498i	$-0.0400527\pi$
$608$		0			0
$609$	−1.62647	−	0.0330620i	−0.0659077	−	0.00133974i
$610$		0			0
$611$	−6.74267	+	11.6787i	−0.272779	+	0.472468i
$612$		0			0
$613$	−24.1162	−	41.7705i	−0.974046	−	1.68710i	−0.683049	−	0.730372i	$-0.739347\pi$
$613$	−24.1162	−	41.7705i	−0.974046	−	1.68710i	−0.290996	−	0.956724i	$-0.593987\pi$
$614$		0			0
$615$	6.88518	−	2.73972i	0.277637	−	0.110476i
$616$		0			0
$617$	8.78843	+	3.19873i	0.353809	+	0.128776i	0.512809	−	0.858503i	$-0.328605\pi$
$617$	8.78843	+	3.19873i	0.353809	+	0.128776i	−0.159000	+	0.987279i	$0.550827\pi$
$618$		0			0
$619$	−28.0779	−	23.5601i	−1.12855	−	0.946962i	−0.129541	−	0.991574i	$-0.541350\pi$
$619$	−28.0779	−	23.5601i	−1.12855	−	0.946962i	−0.999004	+	0.0446122i	$0.985795\pi$
$620$		0			0
$621$	7.23005	+	26.8050i	0.290132	+	1.07565i
$622$		0			0
$623$	−8.58146	−	3.61840i	−0.343809	−	0.144968i
$624$		0			0
$625$	−4.78292	−	27.1253i	−0.191317	−	1.08501i
$626$		0			0
$627$	8.32194	+	6.57267i	0.332346	+	0.262487i
$628$		0			0
$629$	−4.18054	+	7.24092i	−0.166689	+	0.288714i
$630$		0			0
$631$	−13.9183	−	24.1073i	−0.554080	−	0.959695i	−0.997974	−	0.0636158i	$-0.979737\pi$
$631$	−13.9183	−	24.1073i	−0.554080	−	0.959695i	0.443894	−	0.896079i	$-0.353597\pi$
$632$		0			0
$633$	−25.4415	−	8.41480i	−1.01121	−	0.334458i
$634$		0			0
$635$	34.2509	−	28.7399i	1.35921	−	1.14051i
$636$		0			0
$637$	5.72406	−	7.95834i	0.226796	−	0.315321i
$638$		0			0
$639$	31.3374	−	1.85996i	1.23969	−	0.0735788i
$640$		0			0
$641$	6.92065	−	39.2489i	0.273349	−	1.55024i	−0.470808	−	0.882236i	$-0.656038\pi$
$641$	6.92065	−	39.2489i	0.273349	−	1.55024i	0.744157	−	0.668004i	$-0.232851\pi$
$642$		0			0
$643$	−25.1484	+	21.1020i	−0.991756	+	0.832182i	−0.985821	−	0.167800i	$-0.946334\pi$
$643$	−25.1484	+	21.1020i	−0.991756	+	0.832182i	−0.00593505	+	0.999982i	$0.501889\pi$
$644$		0			0
$645$	9.56254	−	17.7583i	0.376525	−	0.699233i
$646$		0			0
$647$	10.9781	−	19.0147i	0.431595	−	0.747545i	−0.565416	−	0.824806i	$-0.691284\pi$
$647$	10.9781	−	19.0147i	0.431595	−	0.747545i	0.997011	+	0.0772613i	$0.0246176\pi$
$648$		0			0
$649$	−0.0802825	−	0.139053i	−0.00315136	−	0.00545832i
$650$		0			0
$651$	−21.8835	−	19.1336i	−0.857682	−	0.749906i
$652$		0			0
$653$	2.08997	+	0.760688i	0.0817870	+	0.0297680i	0.382590	−	0.923918i	$-0.375032\pi$
$653$	2.08997	+	0.760688i	0.0817870	+	0.0297680i	−0.300803	+	0.953686i	$0.597255\pi$
$654$		0			0
$655$	6.87461	−	38.9878i	0.268613	−	1.52338i
$656$		0			0
$657$	−9.59163	+	0.569289i	−0.374205	+	0.0222101i
$658$		0			0
$659$	−5.98914	−	5.02549i	−0.233304	−	0.195765i	0.518639	−	0.854993i	$-0.326439\pi$
$659$	−5.98914	−	5.02549i	−0.233304	−	0.195765i	−0.751943	+	0.659228i	$0.770883\pi$
$660$		0			0
$661$	21.5483	+	7.84293i	0.838130	+	0.305055i	0.725191	−	0.688547i	$-0.241751\pi$
$661$	21.5483	+	7.84293i	0.838130	+	0.305055i	0.112939	+	0.993602i	$0.463973\pi$
$662$		0			0
$663$	−3.05789	+	2.72432i	−0.118759	+	0.105804i
$664$		0			0
$665$	13.3805	+	12.4178i	0.518874	+	0.481541i
$666$		0			0
$667$	1.89675			0.0734423
$668$		0			0
$669$	13.3118	+	10.5137i	0.514665	+	0.406482i
$670$		0			0
$671$	28.9648	+	10.5423i	1.11817	+	0.406981i
$672$		0			0
$673$	2.78773	−	15.8100i	0.107459	−	0.609432i	−0.882750	−	0.469842i	$-0.844311\pi$
$673$	2.78773	−	15.8100i	0.107459	−	0.609432i	0.990210	−	0.139589i	$-0.0445782\pi$
$674$		0			0
$675$	−2.44956	−	1.70915i	−0.0942837	−	0.0657854i
$676$		0			0
$677$	−33.3174	+	12.1265i	−1.28049	+	0.466061i	−0.890595	−	0.454798i	$-0.849712\pi$
$677$	−33.3174	+	12.1265i	−1.28049	+	0.466061i	−0.389897	+	0.920858i	$0.627489\pi$
$678$		0			0
$679$	9.79186	+	19.1044i	0.375777	+	0.733161i
$680$		0			0
$681$	−18.7433	−	14.8035i	−0.718245	−	0.567270i
$682$		0			0
$683$	7.20674	+	12.4824i	0.275758	+	0.477627i	0.970326	−	0.241800i	$-0.0777377\pi$
$683$	7.20674	+	12.4824i	0.275758	+	0.477627i	−0.694568	+	0.719427i	$0.744404\pi$
$684$		0			0
$685$	12.5667	+	21.7661i	0.480147	+	0.831640i
$686$		0			0
$687$	22.5298	+	7.45175i	0.859566	+	0.284302i
$688$		0			0
$689$	13.7892	+	5.01887i	0.525328	+	0.191204i
$690$		0			0
$691$	−3.11995	+	17.6941i	−0.118689	+	0.673117i	0.866169	+	0.499751i	$0.166575\pi$
$691$	−3.11995	+	17.6941i	−0.118689	+	0.673117i	−0.984858	+	0.173365i	$0.944536\pi$
$692$		0			0
$693$	−8.18033	+	14.4786i	−0.310745	+	0.549997i
$694$		0			0
$695$	2.00541	+	1.68274i	0.0760697	+	0.0638301i
$696$		0			0
$697$	0.531255	+	3.01290i	0.0201227	+	0.114122i
$698$		0			0
$699$	−12.6881	+	0.376206i	−0.479909	+	0.0142294i
$700$		0			0
$701$	4.94489			0.186766			0.0933829	−	0.995630i	$-0.470232\pi$
$701$	4.94489			0.186766			0.0933829	+	0.995630i	$0.470232\pi$
$702$		0			0
$703$	7.23552	−	12.5323i	0.272893	−	0.472664i
$704$		0			0
$705$	18.6706	−	34.6726i	0.703174	−	1.30585i
$706$		0			0
$707$	−0.549190	+	0.850127i	−0.0206544	+	0.0319723i
$708$		0			0
$709$	−32.8174	−	27.5371i	−1.23248	−	1.03418i	−0.998074	−	0.0620394i	$-0.980240\pi$
$709$	−32.8174	−	27.5371i	−1.23248	−	1.03418i	−0.234411	−	0.972138i	$-0.575316\pi$
$710$		0			0
$711$	4.43754	−	38.3330i	0.166421	−	1.43760i
$712$		0			0
$713$	25.9629	+	21.7854i	0.972317	+	0.815871i
$714$		0			0
$715$	−1.20300	−	6.82254i	−0.0449895	−	0.255148i
$716$		0			0
$717$	4.04776	+	19.5488i	0.151166	+	0.730062i
$718$		0			0
$719$	−23.6711	+	40.9996i	−0.882784	+	1.52903i	−0.0345523	+	0.999403i	$0.511001\pi$
$719$	−23.6711	+	40.9996i	−0.882784	+	1.52903i	−0.848232	+	0.529625i	$0.822333\pi$
$720$		0			0
$721$	12.0626	+	11.1947i	0.449233	+	0.416911i
$722$		0			0
$723$	−1.90430	+	13.0508i	−0.0708216	+	0.485366i
$724$		0			0
$725$	−0.156321	+	0.131169i	−0.00580562	+	0.00487149i
$726$		0			0
$727$	−1.15931	+	6.57475i	−0.0429963	+	0.243844i	−0.998730	−	0.0503903i	$-0.983953\pi$
$727$	−1.15931	+	6.57475i	−0.0429963	+	0.243844i	0.955733	+	0.294234i	$0.0950646\pi$
$728$		0			0
$729$	26.5741	−	4.77666i	0.984226	−	0.176913i
$730$		0			0
$731$	6.37888	+	5.35252i	0.235931	+	0.197970i
$732$		0			0
$733$	0.385102	+	2.18402i	0.0142241	+	0.0806686i	0.991093	−	0.133168i	$-0.0425150\pi$
$733$	0.385102	+	2.18402i	0.0142241	+	0.0806686i	−0.976869	+	0.213837i	$0.931404\pi$
$734$		0			0
$735$	−16.0193	+	23.7251i	−0.590881	+	0.875115i
$736$		0			0
$737$	15.2813			0.562894
$738$		0			0
$739$	−31.8740			−1.17251			−0.586253	−	0.810128i	$-0.699397\pi$
$739$	−31.8740			−1.17251			−0.586253	+	0.810128i	$0.699397\pi$
$740$		0			0
$741$	5.29247	−	4.71515i	0.194424	−	0.173215i
$742$		0			0
$743$	6.17025	+	34.9932i	0.226364	+	1.28378i	0.860060	+	0.510193i	$0.170426\pi$
$743$	6.17025	+	34.9932i	0.226364	+	1.28378i	−0.633695	+	0.773583i	$0.718463\pi$
$744$		0			0
$745$	−39.1371	+	14.2447i	−1.43387	+	0.521887i
$746$		0			0
$747$	−10.9933	−	8.16531i	−0.402223	−	0.298753i
$748$		0			0
$749$	−5.17056	−	41.2934i	−0.188928	−	1.50883i
$750$		0			0
$751$	20.9742	+	7.63398i	0.765359	+	0.278568i	0.695054	−	0.718958i	$-0.255380\pi$
$751$	20.9742	+	7.63398i	0.765359	+	0.278568i	0.0703052	+	0.997526i	$0.477603\pi$
$752$		0			0
$753$	25.9600	−	0.769719i	0.946034	−	0.0280501i
$754$		0			0
$755$	41.1353			1.49707
$756$		0			0
$757$	−7.66270			−0.278505			−0.139253	−	0.990257i	$-0.544470\pi$
$757$	−7.66270			−0.278505			−0.139253	+	0.990257i	$0.544470\pi$
$758$		0			0
$759$	9.19268	−	17.0715i	0.333673	−	0.619655i
$760$		0			0
$761$	−21.0297	−	7.65420i	−0.762328	−	0.277465i	−0.0685440	−	0.997648i	$-0.521835\pi$
$761$	−21.0297	−	7.65420i	−0.762328	−	0.277465i	−0.693784	+	0.720184i	$0.744058\pi$
$762$		0			0
$763$	12.0941	−	9.15903i	0.437836	−	0.331579i
$764$		0			0
$765$	8.68995	−	8.21672i	0.314186	−	0.297076i
$766$		0			0
$767$	−0.100852	+	0.0367072i	−0.00364156	+	0.00132542i
$768$		0			0
$769$	3.85750	+	21.8770i	0.139105	+	0.788905i	0.971913	+	0.235342i	$0.0756210\pi$
$769$	3.85750	+	21.8770i	0.139105	+	0.788905i	−0.832807	+	0.553563i	$0.813268\pi$
$770$		0			0
$771$	16.6349	+	5.50200i	0.599090	+	0.198150i
$772$		0			0
$773$	−13.8737			−0.499001			−0.249501	−	0.968375i	$-0.580266\pi$
$773$	−13.8737			−0.499001			−0.249501	+	0.968375i	$0.580266\pi$
$774$		0			0
$775$	−3.64631			−0.130979
$776$		0			0
$777$	21.1625	+	8.19333i	0.759201	+	0.293934i
$778$		0			0
$779$	−0.919474	−	5.21460i	−0.0329436	−	0.186832i
$780$		0			0
$781$	−16.7948	−	14.0925i	−0.600964	−	0.504269i
$782$		0			0
$783$	0.157722	−	1.83786i	0.00563652	−	0.0656799i
$784$		0			0
$785$	1.26762	−	7.18905i	0.0452434	−	0.256588i
$786$		0			0
$787$	−0.938744	+	0.787699i	−0.0334626	+	0.0280785i	−0.659366	−	0.751822i	$-0.729175\pi$
$787$	−0.938744	+	0.787699i	−0.0334626	+	0.0280785i	0.625903	+	0.779901i	$0.284731\pi$
$788$		0			0
$789$	−39.8992	+	15.8765i	−1.42045	+	0.565217i
$790$		0			0
$791$	6.11132	−	1.88443i	0.217294	−	0.0670025i
$792$		0			0
$793$	10.3016	−	17.8428i	0.365819	−	0.633617i
$794$		0			0
$795$	−40.6840	−	13.4563i	−1.44291	−	0.477244i
$796$		0			0
$797$	−4.70293	−	26.6716i	−0.166586	−	0.944758i	−0.947414	−	0.320011i	$-0.896313\pi$
$797$	−4.70293	−	26.6716i	−0.166586	−	0.944758i	0.780827	−	0.624747i	$-0.214798\pi$
$798$		0			0
$799$	12.4546	+	10.4506i	0.440611	+	0.369717i
$800$		0			0
$801$	4.72892	−	9.44207i	0.167088	−	0.333619i
$802$		0			0
$803$	5.14048	+	4.31338i	0.181404	+	0.152216i
$804$		0			0
$805$	18.1114	−	28.0358i	0.638344	−	0.988134i
$806$		0			0
$807$	29.1977	−	0.865718i	1.02781	−	0.0304747i
$808$		0			0
$809$	−7.93549	+	13.7447i	−0.278997	+	0.483237i	−0.971136	−	0.238527i	$-0.923335\pi$
$809$	−7.93549	+	13.7447i	−0.278997	+	0.483237i	0.692139	+	0.721764i	$0.256669\pi$
$810$		0			0
$811$	13.9568			0.490088			0.245044	−	0.969512i	$-0.421198\pi$
$811$	13.9568			0.490088			0.245044	+	0.969512i	$0.421198\pi$
$812$		0			0
$813$	−6.71538	+	12.4709i	−0.235519	+	0.437375i
$814$		0			0
$815$	2.77825	+	15.7562i	0.0973179	+	0.551917i
$816$		0			0
$817$	−11.0403	−	9.26392i	−0.386251	−	0.324103i
$818$		0			0
$819$	8.58126	+	7.06534i	0.299854	+	0.246883i
$820$		0			0
$821$	−1.88894	+	10.7127i	−0.0659246	+	0.373877i	0.933940	+	0.357430i	$0.116347\pi$
$821$	−1.88894	+	10.7127i	−0.0659246	+	0.373877i	−0.999865	+	0.0164475i	$0.994764\pi$
$822$		0			0
$823$	−11.9451	−	4.34765i	−0.416379	−	0.151550i	0.125331	−	0.992115i	$-0.460001\pi$
$823$	−11.9451	−	4.34765i	−0.416379	−	0.151550i	−0.541710	+	0.840565i	$0.682223\pi$
$824$		0			0
$825$	0.422955	+	2.04267i	0.0147254	+	0.0711167i
$826$		0			0
$827$	−13.6944	−	23.7193i	−0.476199	−	0.824801i	0.523429	−	0.852069i	$-0.324653\pi$
$827$	−13.6944	−	23.7193i	−0.476199	−	0.824801i	−0.999628	+	0.0272681i	$0.991319\pi$
$828$		0			0
$829$	17.0156	+	29.4719i	0.590976	+	1.02360i	0.994101	+	0.108456i	$0.0345905\pi$
$829$	17.0156	+	29.4719i	0.590976	+	1.02360i	−0.403125	+	0.915145i	$0.632076\pi$
$830$		0			0
$831$	−13.2328	+	5.26552i	−0.459040	+	0.182659i
$832$		0			0
$833$	−8.25065	−	8.46235i	−0.285868	−	0.293203i
$834$		0			0
$835$	43.5159	−	15.8385i	1.50593	−	0.548114i
$836$		0			0
$837$	23.2681	−	23.3453i	0.804262	−	0.806933i
$838$		0			0
$839$	6.05229	−	34.3242i	0.208948	−	1.18500i	−0.682157	−	0.731206i	$-0.738958\pi$
$839$	6.05229	−	34.3242i	0.208948	−	1.18500i	0.891105	−	0.453798i	$-0.149931\pi$
$840$		0			0
$841$	27.1327	+	9.87548i	0.935609	+	0.340534i
$842$		0			0
$843$	−3.73287	+	25.5827i	−0.128567	+	0.881115i
$844$		0			0
$845$	26.0637			0.896620
$846$		0			0
$847$	−16.7129	+	5.15341i	−0.574260	+	0.177073i
$848$		0			0
$849$	−2.22267	−	10.7344i	−0.0762817	−	0.368404i
$850$		0			0
$851$	−24.8632	−	9.04946i	−0.852299	−	0.310211i
$852$		0			0
$853$	32.8722	+	27.5830i	1.12552	+	0.944425i	0.998870	−	0.0475227i	$-0.0151326\pi$
$853$	32.8722	+	27.5830i	1.12552	+	0.944425i	0.126651	+	0.991947i	$0.459577\pi$
$854$		0			0
$855$	−15.0402	+	14.2212i	−0.514365	+	0.486354i
$856$		0			0
$857$	−1.64304	+	9.31815i	−0.0561252	+	0.318302i	−0.999925	−	0.0122146i	$-0.996112\pi$
$857$	−1.64304	+	9.31815i	−0.0561252	+	0.318302i	0.943800	+	0.330517i	$0.107223\pi$
$858$		0			0
$859$	17.8535	+	6.49816i	0.609155	+	0.221714i	0.628133	−	0.778106i	$-0.283819\pi$
$859$	17.8535	+	6.49816i	0.609155	+	0.221714i	−0.0189785	+	0.999820i	$0.506041\pi$
$860$		0			0
$861$	7.85893	−	2.68083i	0.267832	−	0.0913624i
$862$		0			0
$863$	−21.7214	−	37.6225i	−0.739404	−	1.28068i	−0.952764	−	0.303711i	$-0.901774\pi$
$863$	−21.7214	−	37.6225i	−0.739404	−	1.28068i	0.213360	−	0.976974i	$-0.431559\pi$
$864$		0			0
$865$	10.4669	−	18.1292i	0.355886	−	0.616412i
$866$		0			0
$867$	−12.8773	−	20.8515i	−0.437335	−	0.708152i
$868$		0			0
$869$	−20.6448	+	17.3231i	−0.700328	+	0.587645i
$870$		0			0
$871$	1.77370	−	10.0591i	0.0600994	−	0.340841i
$872$		0			0
$873$	−22.3406	+	9.66608i	−0.756113	+	0.327147i
$874$		0			0
$875$	−3.43457	−	27.4294i	−0.116110	−	0.927284i
$876$		0			0
$877$	−16.0388	+	13.4582i	−0.541593	+	0.454451i	−0.872082	−	0.489359i	$-0.837231\pi$
$877$	−16.0388	+	13.4582i	−0.541593	+	0.454451i	0.330489	+	0.943810i	$0.392786\pi$
$878$		0			0
$879$	9.27690	+	44.8030i	0.312902	+	1.51117i
$880$		0			0
$881$	8.40964	+	14.5659i	0.283328	+	0.490739i	0.972202	−	0.234142i	$-0.0752281\pi$
$881$	8.40964	+	14.5659i	0.283328	+	0.490739i	−0.688874	+	0.724881i	$0.741895\pi$
$882$		0			0
$883$	−27.9627	+	48.4328i	−0.941019	+	1.62989i	−0.177485	+	0.984123i	$0.556796\pi$
$883$	−27.9627	+	48.4328i	−0.941019	+	1.62989i	−0.763533	+	0.645768i	$0.776537\pi$
$884$		0			0
$885$	0.291202	−	0.115874i	0.00978866	−	0.00389505i
$886$		0			0
$887$	−5.22280	−	29.6200i	−0.175364	−	0.994541i	−0.937722	−	0.347385i	$-0.887070\pi$
$887$	−5.22280	−	29.6200i	−0.175364	−	0.994541i	0.762358	−	0.647155i	$-0.224041\pi$
$888$		0			0
$889$	39.9406	−	30.2476i	1.33957	−	1.01447i
$890$		0			0
$891$	−15.7771	−	10.3269i	−0.528553	−	0.345963i
$892$		0			0
$893$	−21.5559	−	18.0875i	−0.721340	−	0.605276i
$894$		0			0
$895$	−48.7378	−	17.7391i	−1.62913	−	0.592953i
$896$		0			0
$897$	−10.1705	−	8.03269i	−0.339585	−	0.268204i
$898$		0			0
$899$	−1.12592	−	1.95016i	−0.0375517	−	0.0650414i
$900$		0			0
$901$	8.84580	−	15.3214i	0.294696	−	0.510429i
$902$		0			0
$903$	11.6959	−	19.3392i	0.389214	−	0.643567i
$904$		0			0
$905$	24.5796	−	20.6247i	0.817054	−	0.685590i
$906$		0			0
$907$	−0.772456	+	0.281151i	−0.0256490	+	0.00933547i	−0.354813	−	0.934937i	$-0.615455\pi$
$907$	−0.772456	+	0.281151i	−0.0256490	+	0.00933547i	0.329164	+	0.944273i	$0.393233\pi$
$908$		0			0
$909$	−0.921275	−	0.684282i	−0.0305568	−	0.0226962i
$910$		0			0
$911$	−38.4196	+	13.9836i	−1.27290	+	0.463297i	−0.888077	−	0.459695i	$-0.847959\pi$
$911$	−38.4196	+	13.9836i	−1.27290	+	0.463297i	−0.384820	+	0.922992i	$0.625737\pi$
$912$		0			0
$913$	1.66071	+	9.41833i	0.0549613	+	0.311701i
$914$		0			0
$915$	−28.5252	+	52.9733i	−0.943012	+	1.75124i
$916$		0			0
$917$	9.87578	−	43.2488i	0.326127	−	1.42820i
$918$		0			0
$919$	18.0879	+	31.3292i	0.596665	+	1.03345i	0.993310	+	0.115482i	$0.0368413\pi$
$919$	18.0879	+	31.3292i	0.596665	+	1.03345i	−0.396644	+	0.917972i	$0.629825\pi$
$920$		0			0
$921$	8.47542	−	15.7395i	0.279274	−	0.518633i
$922$		0			0
$923$	−11.2259	+	9.41968i	−0.369506	+	0.310053i
$924$		0			0
$925$	2.67492	−	0.973592i	0.0879509	−	0.0320115i
$926$		0			0
$927$	−13.5588	+	12.8204i	−0.445329	+	0.421078i
$928$		0			0
$929$	2.66423	−	15.1096i	0.0874104	−	0.495729i	−0.909400	−	0.415923i	$-0.863459\pi$
$929$	2.66423	−	15.1096i	0.0874104	−	0.495729i	0.996810	−	0.0798064i	$-0.0254302\pi$
$930$		0			0
$931$	14.2799	+	14.6463i	0.468005	+	0.480013i
$932$		0			0
$933$	−3.99862	−	19.3114i	−0.130909	−	0.632227i
$934$		0			0
$935$	−8.35232			−0.273150
$936$		0			0
$937$	4.51783	−	7.82511i	0.147591	−	0.255635i	−0.782746	−	0.622342i	$-0.786181\pi$
$937$	4.51783	−	7.82511i	0.147591	−	0.255635i	0.930337	+	0.366707i	$0.119515\pi$
$938$		0			0
$939$	−36.2804	+	14.4365i	−1.18397	+	0.471118i
$940$		0			0
$941$	−29.1549	+	24.4638i	−0.950421	+	0.797498i	−0.979368	−	0.202083i	$-0.935229\pi$
$941$	−29.1549	+	24.4638i	−0.950421	+	0.797498i	0.0289472	+	0.999581i	$0.490785\pi$
$942$		0			0
$943$	−9.09759	+	3.31125i	−0.296258	+	0.107829i
$944$		0			0
$945$	−25.6595	−	19.8805i	−0.834703	−	0.646712i
$946$		0			0
$947$	53.2801	−	19.3924i	1.73137	−	0.630167i	0.732642	−	0.680614i	$-0.238287\pi$
$947$	53.2801	−	19.3924i	1.73137	−	0.630167i	0.998727	+	0.0504469i	$0.0160646\pi$
$948$		0			0
$949$	3.43599	−	2.88314i	0.111537	−	0.0935907i
$950$		0			0
$951$	−2.70157	+	18.5148i	−0.0876043	+	0.600384i
$952$		0			0
$953$	−3.06005	+	5.30016i	−0.0991246	+	0.171689i	−0.911323	−	0.411693i	$-0.864938\pi$
$953$	−3.06005	+	5.30016i	−0.0991246	+	0.171689i	0.812198	+	0.583382i	$0.198271\pi$
$954$		0			0
$955$	−22.7352			−0.735695
$956$		0			0
$957$	−0.961882	+	0.856956i	−0.0310932	+	0.0277014i
$958$		0			0
$959$	12.8459	+	25.0630i	0.414815	+	0.809326i
$960$		0			0
$961$	1.60404	−	9.09698i	0.0517433	−	0.293451i
$962$		0			0
$963$	47.1051	−	2.79581i	1.51794	−	0.0900938i
$964$		0			0
$965$	−28.6892	+	10.4420i	−0.923539	+	0.336141i
$966$		0			0
$967$	16.0449	−	13.4632i	0.515968	−	0.432948i	−0.347256	−	0.937771i	$-0.612886\pi$
$967$	16.0449	−	13.4632i	0.515968	−	0.432948i	0.863223	+	0.504822i	$0.168442\pi$
$968$		0			0
$969$	−4.49034	−	7.27095i	−0.144250	−	0.233576i
$970$		0			0
$971$	−29.8737	−	51.7427i	−0.958692	−	1.66050i	−0.725685	−	0.688028i	$-0.758477\pi$
$971$	−29.8737	−	51.7427i	−0.958692	−	1.66050i	−0.233007	−	0.972475i	$-0.574857\pi$
$972$		0			0
$973$	2.15020	+	1.99549i	0.0689321	+	0.0639724i
$974$		0			0
$975$	1.39371	−	0.0413238i	0.0446344	−	0.00132342i
$976$		0			0
$977$	2.26067	+	12.8209i	0.0723251	+	0.410176i	0.999379	+	0.0352470i	$0.0112218\pi$
$977$	2.26067	+	12.8209i	0.0723251	+	0.410176i	−0.927054	+	0.374929i	$0.877667\pi$
$978$		0			0
$979$	−6.93022	+	2.52239i	−0.221491	+	0.0806161i
$980$		0			0
$981$	9.46861	+	14.3617i	0.302310	+	0.458534i
$982$		0			0
$983$	−51.5544	+	18.7643i	−1.64433	+	0.598487i	−0.987788	−	0.155802i	$-0.950204\pi$
$983$	−51.5544	+	18.7643i	−1.64433	+	0.598487i	−0.656542	+	0.754289i	$0.727982\pi$
$984$		0			0
$985$	21.9908	−	18.4525i	0.700687	−	0.587946i
$986$		0			0
$987$	22.8358	−	37.7591i	0.726872	−	1.20189i
$988$		0			0
$989$	−13.1755	+	22.8207i	−0.418958	+	0.725656i
$990$		0			0
$991$	−19.1901	−	33.2383i	−0.609594	−	1.05585i	−0.991307	−	0.131568i	$-0.957999\pi$
$991$	−19.1901	−	33.2383i	−0.609594	−	1.05585i	0.381713	−	0.924281i	$-0.375334\pi$
$992$		0			0
$993$	0.135211	−	0.926647i	0.00429078	−	0.0294063i
$994$		0			0
$995$	−53.7315	−	19.5567i	−1.70340	−	0.619988i
$996$		0			0
$997$	17.3144	+	14.5285i	0.548353	+	0.460123i	0.874383	−	0.485237i	$-0.161267\pi$
$997$	17.3144	+	14.5285i	0.548353	+	0.460123i	−0.326030	+	0.945359i	$0.605711\pi$
$998$		0			0
$999$	−10.8360	+	23.3388i	−0.342836	+	0.738408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bq.a.25.17	yes	144
7.2	even	3		756.2.bp.a.457.1	yes	144
27.13	even	9		756.2.bp.a.445.1	✓	144
189.121	even	9	inner	756.2.bq.a.121.17	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bp.a.445.1	✓	144	27.13	even	9
756.2.bp.a.457.1	yes	144	7.2	even	3
756.2.bq.a.25.17	yes	144	1.1	even	1	trivial
756.2.bq.a.121.17	yes	144	189.121	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bq (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.910101 + 1.47367i) q^{3} +(2.21872 + 0.807546i) q^{5} +(2.43789 + 1.02795i) q^{7} +(-1.34343 + 2.68238i) q^{9} +O(q^{10})\)	\(q+(0.910101 + 1.47367i) q^{3} +(2.21872 + 0.807546i) q^{5} +(2.43789 + 1.02795i) q^{7} +(-1.34343 + 2.68238i) q^{9} +(1.96880 - 0.716583i) q^{11} +(-0.243183 - 1.37916i) q^{13} +(0.829194 + 4.00461i) q^{15} -1.68840 q^{17} +2.92222 q^{19} +(0.703873 + 4.52820i) q^{21} +(-0.927800 - 5.26182i) q^{23} +(0.440344 + 0.369493i) q^{25} +(-5.17562 + 0.461458i) q^{27} +(-0.0616446 + 0.349604i) q^{29} +(-4.85924 + 4.07739i) q^{31} +(2.84781 + 2.24920i) q^{33} +(4.57888 + 4.24943i) q^{35} +(2.47603 - 4.28862i) q^{37} +(1.81111 - 1.61355i) q^{39} +(-0.314649 - 1.78446i) q^{41} +(-3.77805 - 3.17016i) q^{43} +(-5.14685 + 4.86656i) q^{45} +(-7.37654 - 6.18965i) q^{47} +(4.88666 + 5.01204i) q^{49} +(-1.53662 - 2.48816i) q^{51} +(-5.23915 + 9.07447i) q^{53} +4.94687 q^{55} +(2.65952 + 4.30640i) q^{57} +(-0.0133078 - 0.0754723i) q^{59} +(11.2700 + 9.45663i) q^{61} +(-6.03249 + 5.15840i) q^{63} +(0.574182 - 3.25635i) q^{65} +(6.85380 + 2.49458i) q^{67} +(6.90981 - 6.15606i) q^{69} +(-5.23209 - 9.06224i) q^{71} +(1.60142 + 2.77374i) q^{73} +(-0.143754 + 0.985200i) q^{75} +(5.53633 + 0.276860i) q^{77} +(-12.0873 + 4.39941i) q^{79} +(-5.39038 - 7.20721i) q^{81} +(-0.792643 + 4.49530i) q^{83} +(-3.74609 - 1.36346i) q^{85} +(-0.571305 + 0.227331i) q^{87} -3.52003 q^{89} +(0.824847 - 3.61223i) q^{91} +(-10.4311 - 3.45011i) q^{93} +(6.48358 + 2.35983i) q^{95} +(6.21569 + 5.21558i) q^{97} +(-0.722794 + 6.24375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 6 q^{9}+O(q^{10}) \) 144 * q + 6 * q^9	\( 144 q + 6 q^{9} + 6 q^{11} - 12 q^{15} + 48 q^{17} + 33 q^{21} - 21 q^{23} + 6 q^{29} + 18 q^{33} - 9 q^{35} + 9 q^{39} - 12 q^{41} - 12 q^{45} + 18 q^{47} - 18 q^{49} - 9 q^{51} + 15 q^{53} + 3 q^{57} - 15 q^{59} - 36 q^{61} + 3 q^{63} + 36 q^{65} + 30 q^{69} - 12 q^{71} + 18 q^{73} - 51 q^{75} - 3 q^{77} + 18 q^{79} - 6 q^{81} - 36 q^{85} + 33 q^{87} + 144 q^{89} + 9 q^{91} + 48 q^{93} - 30 q^{95} - 72 q^{99}+O(q^{100}) \) 144 * q + 6 * q^9 + 6 * q^11 - 12 * q^15 + 48 * q^17 + 33 * q^21 - 21 * q^23 + 6 * q^29 + 18 * q^33 - 9 * q^35 + 9 * q^39 - 12 * q^41 - 12 * q^45 + 18 * q^47 - 18 * q^49 - 9 * q^51 + 15 * q^53 + 3 * q^57 - 15 * q^59 - 36 * q^61 + 3 * q^63 + 36 * q^65 + 30 * q^69 - 12 * q^71 + 18 * q^73 - 51 * q^75 - 3 * q^77 + 18 * q^79 - 6 * q^81 - 36 * q^85 + 33 * q^87 + 144 * q^89 + 9 * q^91 + 48 * q^93 - 30 * q^95 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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